# Fourier Series / Fourier Transform Question

• SpeedBird
In summary, the conversation discusses drawing a pulse and obtaining its frequency spectrum for an exam question. It includes a description of the pulse and its parameters, as well as a request for ideas and potential solutions. The conversation also briefly touches on an ethics issue and the difficulty of computing the Fourier transform.
SpeedBird
Hello there,

It is part of an exam question.

Firstly I must draw a sketch of this pulse:

v=0 when |t| > a
v=V0( 1 + t/a ) when -a < t <= 0
v=V0( 1 - t/a ) when 0 < t < a

v represents amplitude, V0 represents peak amplitude, t represents
time and 'a' is a constatnt.

i can draw the pulse ok, it is just a triangular pulse that goes from
0 at t = +a and -a to V0 when t = 0.

The bit I am unsure about is obtaining and sketching the frequency
spectrum of this pulse. Any ideas?

Thanks,

Nik

Isn't there an ethics problem with getting assistance with an exam question?

maybe if i was in the exam at the time.
it's a question from last years signal analysis exam.
thanks anyway!

Last edited:
does anyone have any ideas?

Well, have you computed the Fourier transform?

i havnt computed the FT. the integration is huge and i get stuck pretty quickly. do you think getting the Freq spectrum could mean getting $$a_k$$ and $$b_k$$ coefficients for the Fourier series and plotting their magnitudes against $$k$$?

Last edited:
I'm having difficulty seeing the trouble -- the integral should be something straight out of a calc II class, whether you use sines & cosines as your basis, or you use complex exponentials.

## What is a Fourier series?

A Fourier series is a mathematical tool used to represent a periodic function as an infinite sum of sinusoidal functions. It is named after French mathematician Joseph Fourier, who first introduced the concept in the early 19th century.

## What is the difference between a Fourier series and a Fourier transform?

A Fourier series is used to represent a periodic function, while a Fourier transform is used to represent a non-periodic function. The Fourier transform takes into account all frequencies, while a Fourier series only considers the harmonics of a periodic function.

## What are the applications of Fourier series and Fourier transform in science?

Fourier series and Fourier transforms are widely used in various fields of science, such as engineering, physics, chemistry, and biology. They are used to analyze and model periodic and non-periodic signals, such as sound waves, electromagnetic waves, and biological signals.

## What is the relationship between Fourier series and Fourier transform?

A Fourier series can be seen as a special case of a Fourier transform, where the function being represented is periodic. The Fourier transform is a more general representation that can be applied to both periodic and non-periodic functions.

## How is the Fourier transform calculated?

The Fourier transform is calculated by taking the integral of the function over all frequencies. This involves complex mathematical operations, which can be simplified using properties of symmetry and orthogonality of sinusoidal functions.

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